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STAXXXX_Notes_ExamFour

STAXXXX_Notes_ExamFour - Created by Dane McGuckian...

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Created by Dane McGuckian Identifying the Target Parameter Recall: Inferential statistics are used to make predictions and decisions about a population based on information from a sample. The two major applications of inferential statistics involve the use of sample data to (1) estimate the value of a population parameter, and (2) test some claim (or hypothesis) about a population. In this Chapter, we introduce methods for estimating values of some important population parameters. We also present methods for determining sample sizes necessary to estimate those parameters. The unknown population parameter that we are interested in estimating is called the target parameter . Some helpful key words are provided below to determine our target parameter: Parameter Key Words or Phrases Type of Data μ Mean; Average Quantitative p Proportion; Percentage; Fraction; Rate Qualitative Estimating a Population Mean Using a Confidence Interval square6 Recall: A point estimator of a population parameter is a rule or formula that tells us how to use the sample data to calculate a single number that can be used to estimate the population parameter. square6 For all populations, the sample mean x is an unbiased estimator of the population mean μ , meaning that the distribution of sample means tends to center about the value of the population mean μ . square6 For many populations, the distribution of sample means x tends to be more consistent (with less variation) than the distributions of other sample statistics. We have used point estimators before to estimate target parameters; however, we cannot assign any level of certainty with those point estimators. To remove this drawback, we can use what is called an interval estimator . An interval estimator (or Confidence Interval ) is a formula that tells us how to use sample data to calculate an interval that estimates a population parameter. The confidence coefficient is the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times.
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Created by Dane McGuckian z α The diagram shown below shows the coverage of 8 confidence intervals (CI’s). The vertical line shows the location of the parameter μ all the intervals capture the parameter except CI 2. If the confidence level was 95% for each of these intervals we would expect only 5% of the intervals to fail to capture the parameter (as CI 2 has done). The Most common choices for the confidence level are: 90%, 95%, or 99%. ( a = 10%), ( a = 5%), ( a = 1%) A little notation: The value z α is defined as the value of the normal random variable Z such that the area to its right is α . α = area in this tail Our goal for this section is to be able to estimate the true value of the population parameter μ (mu = mean).
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